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The uncritical acceptance of Maslow's need hierarchy theory despite the lack of empirical evidence is discussed and the need for a review of recent empirical evidence is emphasized. A review of ten factor-analytic and three ranking studies testing Maslow's theory showed only partial support for the concept of need hierarchy. A large number of cross-sectional studies showed no clear evidence for Maslow's deprivation/domination proposition except with regard to self-actualization. Longitudinal studies testing Maslow's gratification/activation proposition showed no support, and the limited support received from cross-sectional studies is questionable due to numerous measurement problems. The difficulties with testing the theory are discussed and the conceptual, methodological, and measurement problems of the studies reviewed are detailed. The implications of the findings and future directions for research are outlined.

Neher (1991, FREE PDF) summarises and critically evaluates the theory. From the abstract:

This critique of Maslow's theory of motivation examines all of its
major components. The theory is summarized and its basic propositions
are analyzed in the light of internal logic, other relevant theories,
and related research. This examination points up many deficiencies in
Maslow's theory, which enjoys wide acceptance, especially among
humanistic psychologists. Suggestions are made regarding modifications
to the theory that would remedy many of its more serious problems but
at the same time preserve its perceptive insights.

The hierarchy of needs is an observation made by Maslow. It's generally assumed as the model to go by because most people can agree with the list and its order. Therefor it's no longer just a hypothesis, it's a theory.

In the reference provided by Richard (i.e., Wahba and Bridwell, 1976) it reports studies where people did not agree on the order); There's also an interesting article "Rediscovering the later version of Maslow's hierarchy of needs" FREE PDF where Kolko-Rivera argues that Maslow proposed a level above self-actualisation called self-transcendence.
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Jeromy Anglim♦Jan 27 '12 at 0:39

In Maslow's (1943) original article, he proposed the "desires to know and understand" as well. I've often felt this worth mentioning as an underemphasized element of the original theory. "The desire to know and to understand are themselves conative, i.e., have a striving character, and are as much personality needs as the 'basic needs' we have already discussed."
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Nick StaunerJan 30 '14 at 13:57

TL;DR: tons of support (and complications) at each level. One sequence can't fit all (it didn't claim to), but it makes sense in general, and so do the exceptions, and so do other motive models.

Check out Kenrick and colleagues' (2010) recent article. Kenrick is a prominent evolutionary psychologist; he and his colleagues have "renovated" Maslow's motive hierarchy based on a little bit of everything, including evolutionary, biological, personality, social, and cultural psychology. It's got some speculative theoretical claims of its own, but offers a deep review of empirical research too, and attempts to synthesize them. I'll just quote some of the parts that reference other research here (without vouching that all of it is necessarily original or empirical) to give you a sense of where else you might look beyond this article itself, and how Kenrick and colleagues summarize their basic findings directly. They go much further than direct summary though, so as other answers here have noted, there are many alternatives to Maslow's (1943) original theory, including this one!

An updated hierarchy of fundamental human motives...integrates ideas from life-history development with Maslow’s classic hierarchy...adds reproductive goals, in the order they are likely to first appear developmentally...[and] depicts the later developing goal systems as overlapping with, rather than completely replacing, earlier developing systems. Once a goal system has developed, its activation will be triggered whenever relevant environmental cues are salient. [Emphasis added.]

The overlapping triangles...explicitly reflect...that later developmental needs and goals add to, rather than replace, existing ones...

Summary of Developmental Level of Analysis

Developmental...life-history theory suggest[s]...revisions to Maslow’s original hierarchy...Three later-developing reproduction-focused goals of mate acquisition, mate retention, and parental care...different motives in the hierarchy continue to operate alongside those that develop later in life...reflected visually by the overlapping triangles...Important individual differences in motivational priorities...result from interactions between development and current environment...

Conclusion

Developments [in] evolutionary biology, anthropology, and psychology...suggested...structural modifications to Maslow’s classic hierarchy of human motives...The ultimate functions of behaviors and of life-history development [suggest] explicit inclusion of motivational levels linked to mating and reproduction. Reproduction...is not ultimately about self-gratification, but involves a considerable diversion of resources away from selfish goals and toward other[s]...Life-history trade-offs also [imply] that later developing motive systems never fully replace earlier ones...they continue to coexist, ready to be activated depending on current opportunities and threats in the environment, in interaction with individual differences. Thus...the ongoing dynamic interaction between internal motives and their functional links to ongoing environmental threats and opportunities.

Interested readers may find my original version more useful. It includes a comprehensive summary of Kenrick and colleagues' (2010) empirical research literature review, which covers a LOT more independent research that's relevant to individual elements of Maslow's (1943) original theory. Because I included this in the form of boiled-down excerpts rather than paraphrased writing of my own, I've cut it out of the present version to avoid potential problems with fair use law regarding even public domain work such as this. Nonetheless, the original version remains accessible, and hopefully legal.
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Nick StaunerJan 31 '14 at 21:21